Question: Simplify the following expression: $\dfrac{54r^5}{45r}$ You can assume $r \neq 0$.
Explanation: $ \dfrac{54r^5}{45r} = \dfrac{54}{45} \cdot \dfrac{r^5}{r} $ To simplify $\frac{54}{45}$ , find the greatest common factor (GCD) of $54$ and $45$ $54 = 2 \cdot 3 \cdot 3 \cdot 3$ $45 = 3 \cdot 3 \cdot 5$ $ \mbox{GCD}(54, 45) = 3 \cdot 3 = 9 $ $ \dfrac{54}{45} \cdot \dfrac{r^5}{r} = \dfrac{9 \cdot 6}{9 \cdot 5} \cdot \dfrac{r^5}{r} $ $\phantom{ \dfrac{54}{45} \cdot \dfrac{5}{1}} = \dfrac{6}{5} \cdot \dfrac{r^5}{r} $ $ \dfrac{r^5}{r} = \dfrac{r \cdot r \cdot r \cdot r \cdot r}{r} = r^4 $ $ \dfrac{6}{5} \cdot r^4 = \dfrac{6r^4}{5} $